Horizontal spring, mass and nonconstant friction

[Siune]

Homework Statement

Hello! The problem is about spring with block attached to it. ( with spring constant = k) The system is on surface that has a friction μ increasing towards the direction of the blocks movement.

Block is pushed -0,1m ( to the left ) from the equilubrium position and then released. The block moves from the starting position, +0,3m to the right ( +0,2m from the equilubrium position) and stops. What is the spring constant k?

Homework Equations

Spring constant = k
Friction μ = 0,025 * x, increasing towards to the right.
Mass of the block = 2,7 kg

The Attempt at a Solution

The most problematic part for me is the friction not being constant.

I assume;

From -0,1 m to 0,0 m the Force due to the spring and Force due to the friction are in different directions.

From 0,0 m to 0,2 m the Force due to the spring and Force due to the friction are in same direction.

I'm not sure, but as the accelereation ain't constant ( due to the both forces depending on some variable) should I be using some definite integrals?

Or should I use some energy-theorem involving kinetic-energy and potential-energy?

Sincerely yours,
Siune

P.S I can draw a picture about the situation and scan it here, if the explanation ain't good enough. English isn't my native language. :)

 

[tiny-tim]

Hi Siune!

… should I use some energy-theorem involving kinetic-energy and potential-energy?

yes, use the work energy theorem (and a bit of integration) …

(KE + PE)_initial - (KE + PE)_final = work done by friction ​